A simple expression for estimating attenuation by fog at millimeter wavelengths

At millimeter wavelengths, fog attenuation is a function of the fog density, extent, index of refraction of the fog medium, and wavelength. The attenuation is usually determined by first estimating the index of refraction of water for the wavelength and temperature of interest and then calculating the attenuation using the Rayleigh approximation. In this communication fog attenuation is computed for a large set of wavelengths and indices of refraction. A regression analysis of the attenuation is then conducted as a function of wavelength and temperature. It is shown that an almost perfect fit can be obtained with a four-term regression on wavelength and temperature for the ranges of 3 mm < cm and C C, respectively 5666. This expression produces a normalized fog attenuation; the total attenuation is easily computed by multiplying the normalized attenuation by the fog density and extent. If fog density data are not available, a formula for estimating the density from fog visibility is given.